1. Field of the Invention
This invention relates to apparatus and methods for high-order harmonic generation (HHG) from ions in a capillary discharge plasma. In particular, the present invention relates to HHG in a capillary discharge wherein an electric discharge is used to pre-ionize the medium for the driving laser.
2. Description of Related Art
High-order harmonic generation (HHG) has proven to be a useful source of coherent extreme ultraviolet (EUV) and soft x-ray radiation. Several applications of HHG light have been demonstrated to date, such as the investigation of surface dynamics [1, 2], probing static molecular structure and internal molecular dynamics [3, 4], the study of nonlinear optic effects at EUV wavelengths [5], as well as holographic [6] and photo-acoustic [7] imaging. When a medium is illuminated by an intense laser field, odd-order harmonics of the fundamental laser are generated. The highest photon energy that can be produced through this process is predicted by the cutoff rule to be hνmax=Ip+3.17 Up, where Ip is the ionization potential of the target atom and Up is the ponderomotive energy of the liberated electron in the laser field [8]. (Up=E2/4ω2 in atomic units where E is the peak of the laser electric field with frequency ω). In principle with long wavelength or high field lasers, hνmax may be as high as 10 keV or greater before relativistic effects suppress re-scattering and HHG [9].
To date however, for many experiments the highest harmonic photon energies observed have not been limited by the available laser intensity, but rather by the ionization of the nonlinear medium by the driving laser. The depletion of neutrals does not terminate the harmonic emission since high harmonics may also be generated from ions. Rather, the electron density from photo-ionization refractively defocuses the driving laser, reducing the peak laser intensity and consequently the highest harmonic photon energy observed. Moreover, the resulting plasma imparts different phase velocities to the driving laser and the HHG light, which results in poor phase-matching and conversion efficiency. Finally, the loss of the laser energy due to photo-ionization limits the length in the medium over which a high peak intensity can be maintained.
In past experiments, extremely short laser pulses, [10] and target atoms with high ionization potential [11] were employed to obtain the highest possible photon energies, since both of these characteristics allows neutral atoms to survive to higher laser intensities. Seres et al. recently demonstrated that harmonics with photon energies up to >1 keV can be obtained by using intense 12 fs laser pulses focused into a He gas cell [12]. Although nonadiabatic effects may help to ameliorate the very short coherence length in these experiments, [13] the high harmonic flux produced is nevertheless very low. Another method to extend harmonics to higher photon energies is to generate harmonics from ions rather than neutral atoms [14, 15]. Ions have higher ionization potentials than neutrals and therefore ionize at much higher laser intensities. Gibson et al. demonstrated that significantly higher harmonics, up to 250 eV, can be generated from Ar ions by confining the driving laser beam in a gas-filled hollow waveguide. The use of a hollow waveguide greatly reduces ionization-induced defocusing, allowing a significant extension of the cutoff photon energy.
Harmonic generation in a preformed plasma with a tailored density profile can further enhance harmonic generation from ions. The use of preformed plasma waveguides for HHG has been previously proposed [16, 17], but was not demonstrated experimentally until recently. Capillary discharges provide a convenient way to generate plasma waveguides with a tailored degree of ionization in numerous gases and vapors [17-20], in which the generation of high harmonics from ions can extend efficient coherent light generation to shorter wavelengths. In recent work, we demonstrated that a significant extension of the HHG cutoff in Xe can be obtained using a capillary discharge to produce a preformed, fully-ionized plasma [21]. In that work, the range of photon energies generated in Xe was extended to ˜150 eV, well above the highest previously-observed value of ˜70 eV [22].
Subsequent experiments expanded on these findings by extending high harmonic generation from Xe, Kr, and Ar using a capillary discharge, to photon energies well beyond what have been previously observed. Harmonic emission from Kr and Ar in a discharge medium was demonstrated. Our results show that in all three gases, the cutoff energy for HHG is enhanced in a capillary discharge beyond what is possible in a capillary without the discharge.
By combining experimental measurements of the harmonic spectrum and of the transmitted laser pulse with a hydrodynamic model of the discharge plasma, we showed HHG emission from ions is extended and enhanced because of improved laser transmission through the waveguide. When high harmonics are to be generated from interaction of the intense laser with ions, rather than with neutral atoms, pre-ionizing the medium results in reduced ionization-induced defocusing, decreased ionization losses, and reduced self-phase modulations and other pulse distortions that can limit the efficiency of high harmonic generation. Moreover, the ionized medium created by the discharge also provides a method to spectrally tune the harmonics by tailoring the initial level of ionization of the medium.
A need remains in the art for apparatus and methods for efficient high-order harmonic generation from ions in a capillary discharge wherein an electric discharge is used to pre-ionize the medium for the driving laser, generating coherent light at shorter wavelengths.